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All the numbers from 100,000 to 111,111 contain a zero, so that is 11,111 numbers already. The question is then how many numbers between 1,111 and 2,000 contain at least one zero. There are 19 numbers every hundred digits from 1,200 onwards that meet this requirement (10 which have a 0 in the tens and ten which have a 0 in the units, not counting 00 twice) and thus we have 19x8 = 152 additional numbers. Add this to the amount from before, and 1 for the end value of 112,000: 11,111+152+1 = 11,264 numbers.

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Q: How many numbers from 100000 to 112000 contain at least one zero?
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